Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Upcoming SlideShare
×

# 17.04.2012 m.petrov

1,526 views

Published on

Published in: Education, Technology
• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Be the first to comment

• Be the first to like this

### 17.04.2012 m.petrov

1. 1. Polariton spin transport in a microcavity channel:A mean-ﬁeld modelingM.Yu.Petrov1 and A.V.Kavokin1,21Spin Optics Laboratory, Saint Petersburg State University, Russia2Physics and Astronomy School, University of Southampton, UK SOLAB seminar, Apr. 17, 2012
2. 2. Outline• Motivation for experimentalists• Mean-ﬁeld model and its numerical implementation• Results of modeling • Interference of two ﬂows in a channel • Spin-polarized polariton transport in a channel • Interpretation in terms of spin conductivity• Summary and further steps
3. 3. Motivation for experimentalists pump-L pump-R Quantum Well Bragg Mirrors
4. 4. Mean-ﬁeld model ↵2 = 0.1↵18 ⇣ 2 ⌘<iù @ ù iù @t + (x, t) = r2 + ↵1 | 2 + (x, t)| + ↵2 | (x, t)|2 + (x, t) + p+ (x, t) ⇣ 2m 2⌧ ⌘:iù @ ù2 iù @t (x, t) = 2m r2 + ↵1 | (x, t)|2 + ↵2 | + (x, t)| 2 2⌧ (x, t) + p (x, t) ⌧ 10ps 5 m 3 ⇥ 10 m0 (x xL )2 L p± (x, t) =p± e x2 eiwL t+ikL ·x + (x xR )2 R p± e x2 eiwR t+ikR ·x
5. 5. Numerical implementation• Spatial discretization by using Finite Element Method • Quadratic elements • Grid size: ∆x<0.25µm @ Lch~100µm• Time discretization u0 = f (t, u), u(t0 ) = u0 ; • 5-step Backward Differentiation Formula s X ak un+k = h f (tn+s , un+s ); k=1 • Max time step: ∆t<100fs @ τ=10ps tn = t0 + nh.• Implementation using Comsol (2D and 1D) and a private software (1D)
6. 6. Interference of two pump pulses
7. 7. Interference of two pump pulses (2)current density iù ⇤ ⇤ j= ( ±r ± ±r ±) 2m
8. 8. Interference of two pump pulses (2)current density iù ⇤ ⇤ j= ( ±r ± ±r ±) 2m
9. 9. Spin-polarized polariton transport
10. 10. Spin-polarized polariton transport
11. 11. Spin-polarized polariton transport 2 2 | +| | |⇢c = | + |2 +| |2
12. 12. Conductivity tensor @ ⇣ ù2 2 iù ⌘ 2 2 iù ± = r + ↵1 | ±| + ↵2 | ⌥| ± + P± @t 2m 2⌧ p ± = n± ei± @n± Imaginary part of GP eq. decomposition gives: + div j = 0 @t ù h n+ r+ i ⇣ ⌘h + + µR µL i j= n r = ++ + µR µL m + (x x0 )2 ± (x, t) = ± (x)e iµ± t/ù P± = p0 e 2 ei!± t/ù+ik± ·x ⇣ ù2 2 iù ⌘ 2 2 0 µ± ± (x) = r + ↵1 | ±| + ↵2 | ⌥| ± (x) + P± (x) 2m 2⌧
13. 13. Spin-current density with diferent pump-pulses h ù n+ r+ i ⇣ ⌘h + + i µR µL j= n r = ++ + µR µL m +
14. 14. Summary and further steps• A mean-ﬁeld model describing polariton spin transport based on coupled Gross-Pitaevskii equations is developed • Numerical implementation of the model demonstrates interference of two ﬂows stimulated by CW excitation near both boundaries of a channel • If pumps are cross-polarized the effect can be emphasized by detection of circular polarization degree• Further steps • Possibility of experimental observation